Technical Field
Embodiments of the subject matter disclosed herein generally relate to seismic data processing or, more specifically, to applying surface-consistent frequency-dependent phase corrections.
Discussion of the Background
In geophysical prospecting, gas and oil reservoirs are sought by performing seismic surveys of underground formations. Trajectory of waves injected in the explored formation is affected by variations of seismic wave propagation velocity from one layer to another. At layers interfaces, the waves may be reflected, refracted and/or transmitted. The waves emerging from the formation are detected by seismic receivers. Seismic surveys are performed on land and in water.
The near surface variations cause time delays and frequency dependent phase distortions in the detected waves. These alterations (i.e., the time delays and the frequency dependent phase distortion) undesirably corrupt the sought underground structural information.
Conventionally, the time shifts have been corrected by fitting a surface consistent model to time anomalies of a particular event on various traces:Δti=S(si)+G(gi)+Y(yi)+R(yi)hi2  (1)where Δti is the time anomaly for a trace resulting from a shot si and detected by receiver gi, corresponding to mid-point yi=(si+gi)/2, and a shot-receiver offset hi=(si−gi)/2, S and G are shot and receiver corrections, Y is a structure term and R is a residual normal-moveout (NMO) correction. The time anomalies (used to determine functions S, G, Y and R) may be picked using cross-correlation maxima. However, this non-linear method of picking maxima is susceptible to failure in the presence of ambiguity or noise. Alternatively or additionally, another method (described in the article “Surface-consistent residual statics by stack power maximization” by J. Ronen and J. F. Claerbout, published in Geophysics 50, No. 12, 1985, pp 2,759-2,767, the entire content of which is incorporated herein by reference) seeks maximization of the stack-power. In this approach, the time shift corresponds to a linear phase with null intercept in the frequency domain.
Conventional methods (as described in the article “Mixed phase surface consistent deconvolution without phase unwrapping” by R. Calvert and C. Perkins, published in proceeding of EAGE 63RD Conference & Technical Exhibition, 2001, the entire content of which is incorporated herein by reference) assume a minimum phase input or require phase unwrapping. The assumption is not necessarily correct and the phase unwrapping is complex and susceptible to introduce errors.
Since correction of the time and phase distortions caused by near-surface variations are a prerequisite for inversion and 4-D analysis (i.e., comparing seismic datasets acquired for the same area at time intervals large enough to make possible observing substantive changes inside the surveyed formation), it is desirable to develop methods able to make more accurate surface related corrections, while mitigating the above-identified drawbacks of the conventional methods.